The numerical value of `"tan"(2tan^(-1)(1/5)-pi/4`is equal to____

1.	The numerical value of `"tan"(2tan^(-1)(1/5)-pi/4`is equal to____
Answer» Correct Answer - `(- (7)/(17))` ` tan [ 2 tan ^(-2) ((1)/(5)) - (pi)/(4)] = tan [ tan ^(-1) (( 2* (1)/(5))/( 1 - ( 1)/( 25))) - (pi)/(4)]` `" "= tan [ tan ^(-1) ((5)/( 12)) - (pi)/( 4)] ` ` " " = ( tan [ tan ^(-1) ((5)/( 12)) ] - tan (( pi)/( 4)))/( 1 + tan [ tan ^(-1) ((5)/( 12)) ] tan ""(pi)/( 4))` ` " " = ((5)/( 12) - 1 )/( 1 + ( 5)/( 12) * 1) = - ( 7)/( 17)`

Discussion

If `alpha=3sin^-1(6/11) `and `beta=3cos^-1(4/9)`, where the inverse trigonometric functions take only the principal values, then the correct option(s) is (are)A. `cos beta gt 0`B. ` sin beta lt 0`C. ` cos ( alpha + beta) gt 0`D. ` cos alpha lt 0`
if `cos^(-1)((2)/(3x))+cos^(-1)((3)/(4x))=(pi)/2, x>3/4` then `x=` (a) `(sqrt(145))/(11)` (b) `(sqrt(145))/(12)` (c) `(sqrt(146))/(10)` (d) `(sqrt(146))/(11)`A. `(sqrt ( 145))/( 10 )`B. `( sqrt ( 146))/( 12)`C. ` (sqrt ( 145))/( 12)`D. `(sqrt ( 145))/( 11)`
The number of real solutions of `tan^(-1)sqrt(x(x+1))+sin^(-1)sqrt(x^2+x+1)=pi/2`is`z`ero b. one``c. twod. infiniteA. zeroB. oneC. twoD. infinite
The numerical value of `"tan"(2tan^(-1)(1/5)-pi/4`is equal to____
Let `tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^2))`, where `|x|
Solve the equation `tan^(-1)2x+tan^(-1)3x=pi/4`
The value of `cot {sum_(23)^(n=1) cot^(-1)(1+ sum_(n=1)^(n) 2k)}` isA. `(23)/(25)`B. `(25)/(23)`C. `(23)/(24)`D. `( 24)/(23)`